Generalized framework for spherical microphone arrays: Spatial and frequency decomposition

This paper provides a generalized framework to decompose a sourcefield into its spatial and frequency components using a spherical microphone array. Spherical arrays are used to decompose a soundfield into spherical harmonics which are the natural basis functions for space over directions. This paper extends this theory by including basis functions in frequency to decompose a soundfield into spatial-frequency components. Specifically, we use spherical Bessel functions as a set of basis in frequency. The paper also shows how to avoid numerical ill-conditioning inherited in open spherical arrays at frequencies corresponding to Bessel zeros.